The functions $f(x) = 2^x$, $f(x) = 2 · 2^x$, and $f(x) =\frac { 1 } { 2 } \cdot 2^x$ all have the same multiplier.   

1. What is the multiplier for these functions? Make an $x → f(x)$ table for each of the functions, using integer values of $x$ for $x = −3$ to $x = 5$. How can you use the tables to determine the multiplier?

   Hint (a):

   For example, compute $f(1)$ and $f(2)$. What number do you need to multiply $f(1)$ by to get $f(2)$?

2. On the same set of axes, sketch the three functions. Describe the similarities and differences among the graphs.

   Hint (b):

   Compare the general shapes, intercepts, asymptotes, and growth rates.